For years, Republicans savaged Democrats for supporting the Affordable Care Act, branding the law — with some rhetorical license — as a government takeover of health care.

Now, cast out of power in Washington and most state capitals, Democrats and activist leaders seeking political redemption have embraced an unlikely-seeming cause: an actual government takeover of health care.

At rallies and in town hall meetings, and in a collection of blue-state legislatures, liberal Democrats have pressed lawmakers, with growing impatience, to support the creation of a single-payer system, in which the state or federal government would supplant private health insurance with a program of public coverage. And in California on Thursday, the Democrat-controlled State Senate approved a preliminary plan for enacting single-payer system, the first serious attempt to do so there since then-Gov. Arnold Schwarzenegger, a Republican, vetoed legislation in 2006 and 2008.

With Republicans in full control of the federal government, there is no prospect that Democrats can put in place a policy of government-guaranteed medicine on the national level in the near future. And fiscal and logistical obstacles may be insurmountable even in solidly liberal states like California and New York.

Yet as Democrats regroup from their 2016 defeat, leaders say the party has plainly shifted well to the left on the issue, setting the stage for a larger battle over the health care system in next year’s congressional elections and the 2020 presidential race. Their liberal base, emboldened by Senator Bernie Sanders’s forceful advocacy of government-backed health care last year, is increasingly unsatisfied with the Affordable Care Act and is demanding more drastic changes to the private health insurance system.

In a sign of shifting sympathies, most House Democrats have now endorsed a single-payer proposal. Party strategists say they expect that the 2020 presidential nominee will embrace a broader version of public health coverage than any Democratic standard-bearer has in decades.

RoseAnn DeMoro, the executive director of National Nurses United and the California Nurses Association, powerful labor groups that back single-payer care, said the issue had reached a “boiling point” on the left.

Supporters of universal health care, including activists with Ms. DeMoro’s union, repeatedly interrupted speakers at the California Democratic Party’s convention in May, challenging party leaders to embrace socialized medicine. Demonstrators waving signs with single-payer slogans have become a regular feature at town hall meetings hosted by members of Congress.

“There is a cultural shift,” said Ms. DeMoro, who was a prominent backer of Mr. Sanders. “Health care is now seen as something everyone deserves. It’s like a national light went off.”

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Representative Rick Nolan, Democrat of Minnesota, campaigning in Duluth, Minn., last year. He said he supported creating a single-payer system in his state but believed the party’s goal should be a national law.CreditTom Williams/CQ Roll Call, via Associated Press

Representative Rick Nolan of Minnesota, a populist Democrat whose district voted for President Trump by a wide margin, said he had rarely seen core Democratic voters as enthusiastic about an issue as they were about single-payer health care. Mr. Nolan said he would support creating a state-level system in Minnesota, but believed the party’s goal should be a national law.

He warned Democrats against being too cautious on health care or trusting that they could passively reap the benefits of Republican missteps, saying that his party needed a more boldly “aspirational” health care platform.

Rank-and-file Democrats, Mr. Nolan said, “are energized in a way I have not witnessed in a long, long time.”

At this point, state and federal single-payer proposals appear mainly to embody the sweeping ambitions of a frustrated party, rather than to map a clear way forward on policy. A handful of legislators in Democratic states — some positioning themselves to run for higher office — have proposed single-payer bills, including in New York, New Jersey, Rhode Island and Massachusetts. Only in California does the legislation appear to have at least a modest chance of being approved this year.

Even there, State Senator Ricardo Lara, an author of the bill, said his legislation would not clear the State Assembly without detailing how expanded coverage would be financed. The proposal currently lacks a complete funding plan.

The bill would mandate far more comprehensive access to health care, with no out-of-pocket costs, for all California residents at an estimated cost of $400 billion annually. Roughly half would come from existing public money spent on health care, but the rest would require new taxes. Gov. Jerry Brown, a Democrat who once campaigned for president supporting single-payer care, has questioned how the state can plausibly foot the bill.

Should California enact a single-payer law, it would still require a waiver from Washington to redirect federal funding to the state program — which might be difficult with Trump appointees running the Department of Health and Human Services.

But Mr. Lara said that Mr. Trump’s election, and subsequent Republican efforts to unwind the Affordable Care Act, had upended the conversation about health care among Democrats. He said he would have been unlikely to press for single-payer under a Democratic president.

“I no longer have the luxury of going step by step,” Mr. Lara said. “We need to do a single-payer or we’re going to be in a position where millions of people are going to lose coverage.”

There remains considerable skepticism among senior Democrats about a single-payer plan, and party strategists fear that proposing a potentially divisive health care agenda would offer Republicans a welcome diversion from their own tortured wrangling over the Affordable Care Act.

At a briefing with reporters last month, the House minority leader, Representative Nancy Pelosi of California, replied with a flat “no” when asked if Democrats should make single-payer a central theme in 2018. She said state-level action was more appropriate, though she said she supported the idea in concept.

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RoseAnn DeMoro, right, the executive director of National Nurses United and the California Nurses Association, in 2014. She said the issue, which her groups support, had reached a “boiling point” on the left.CreditJim Wilson/The New York Times

“The comfort level with the broader base of the American people is not there yet,” Ms. Pelosi said.

In the past, top Democrats — including President Barack Obama and Hillary Clinton — have suggested more incremental approaches, proposing the creation of an optional government health plan that people could buy into or lowering the eligibility age for Medicare.

Democrats were unable to pass either of those measures into law the last time they controlled Congress and the White House, in 2010, because they failed to draw unanimous support from both liberal and centrist Democrats. Mr. Obama never tried to create a full single-payer system, and Mrs. Clinton described the idea as unachievable during the 2016 campaign.

A study published in January by the Pew Research Center found that about 40 percent of Democrats favored a single-payer system, including a slight majority of self-described liberal Democrats. Among all Americans, support was markedly lower: Just 28 percent said government should be the sole provider of care.

But a sizable majority — about three in five Americans — said the government had a responsibility to ensure everyone had health care. And the idea of single-payer health care has stirred interest among some business leaders, like Warren E. Buffett and Charles Munger, who see health care costs as a drag on the economy.

Karen Politz, a senior fellow at the Kaiser Family Foundation who has tracked the single-payer debate for years, said it would be difficult to persuade the country to move to an all-government health care system — a disruptive process that would likely lead to higher taxes in place of the premiums people now pay to insurance companies.

Even if most consumers paid less over all, as single-payer proponents claim, Ms. Politz said, morphing premiums into taxes would be culturally and politically challenging. “It does involve big government, and it’s kind of baked into the American psyche that we resist that,” she said.

Still, Democrats acknowledge that there is a palpable appetite on the left for comprehensive government health care. A number of the party’s potential 2020 presidential contenders, including Senators Cory Booker of New Jersey and Kamala Harris of California, have signaled support for some version of universal government care, though neither Mr. Booker nor Ms. Harris has endorsed the single-payer proposal in his or her home state.

In the House, 112 of the 193 Democrats have co-sponsored a single-payer bill proposed by Representative John Conyers Jr. of Michigan and called the “Expanded and Improved Medicare for All Act.” Until recently, the bill had attracted a fraction of that support.

The Conyers proposal would effectively void the current private health insurance system and impose new taxes on wealthy people and on certain kinds of income to pay for benefits. In May, the bill won a symbolically telling endorsement from Representative Joseph Crowley of New York, the chairman of the Democratic caucus and a leading possible successor for Ms. Pelosi.

Mr. Crowley said his support for the bill was “part practical, part aspirational,” conceding that there was no immediate path to making it law.

“You can’t do this with 110 votes,” he said.

A version of this article appears in print on , on Page A1 of the New York edition with the headline: Inching to Left, Democrats Push Universal Care. Order Reprints | Today’s Paper | Subscribe